Free Access Vychislitel'naya Seysmologia Index Book Editor(s):Dipak K. Chowdhury, Dipak K. ChowdhurySearch for more papers by this authorJean-Claude De Bremaecker, Jean-Claude De BremaeckerSearch for more papers by this authorKashhaiar Lashgari, Kashhaiar LashgariSearch for more papers by this authorEdo Nyland, Edo NylandSearch for more papers by this authorRobert Odom, Robert OdomSearch for more papers by this authorMrinal Sen, Mrinal SenSearch for more papers by this authorM. M. Vishik, M. M. VishikSearch for more papers by this authorV. I. Keilis-Borok, V. I. Keilis-BorokSearch for more papers by this authorA. L. Levshin, A. L. LevshinSearch for more papers by this authorG. M. Molchan, G. M. MolchanSearch for more papers by this authorB. M. Naimark, B. M. NaimarkSearch for more papers by this author First published: 01 January 2003 https://doi.org/10.1002/9781118669655.oth1Book Series:Computational Seismology and Geodynamics AboutPDFPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShareShare a linkShare onEmailFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Selected Papers From Volume 30 of Vychislitel'naya Seysmologiya, Volume 5 RelatedInformation
There have been attempts to investigate the multifractal nature of physical objects like earthquake epicenters, star clusters, etc. This is modeled here using a rigorous mathematical analysis of the fine fractal structure of zeroes Z of Brownian motion w(t), t > O. We use a natural measure of local time of w(t) on Z and demonstrate that it is a multifractal set with a linear spectral function in the range [1/2, 3/4]. The choice of a measure on a fractal is a procedure that depends on the author's judgement. For this reason we consider Z as the limit of the images Zϵ with varying degrees of point resolution ϵ, ϵ ↓ 0. The elements of Zϵ are intervals (ϵ-clusters) containing points with interpoint distances less than ϵ. It is shown that the number of ϵ-clusters of diameter ϵα (α-type) grows like ϵ−ƒ(α), where ƒ(α) is a linear function in the interval [1, 2]. The object Z is interesting in that ϵ-clusters of α-type have unexpected limits as ϵ ↓ 0. The correct result is obtained from upper (unobservable) limits of Zϵn, ϵn = c−n, c >1, n = 1,2, … or lower limits of Zϵn for ultrafast (practically unrealistic) decrease of ϵn: ϵn/ϵn+1 → ∞.
We calculate the variations of temperature fields in magma chambers and the surrounding material. In a suggested two-dimensional model, a viscous hot melt occupies a horizontal layer (a magma chamber) within a thicker solid layer. The geometry of this system and a temperature gradient in its solid part are initial conditions. Thermal convection starts in the melt and the magma chamber begins to cool, owing to heat loss through conduction in the surrounding solid medium. Melting occurs at liquid/solid interfaces, followed by solidification of the melt. We solve equations of thermal convection and heat conduction in liquid and solid regions, respectively. Numerical solutions are obtained by the single-region method where equations are applied to the whole region and the moving phase boundary results from calculations. The problem so formulated reduces to generalized equations of thermal convection with the effective heat capacity which includes heat generation in the Stefan problem. An additional function enters the right-hand side of the Stokes equation. This function is such that generalized equations reduce to the usual equations of thermal convection within the melt and to the heat conduction equation in the solid part of the system. We calculate thermal regimes of magmatic chambers for various geometries. We also obtain time dependence of heat flows at liquid/solid interfaces; and at the Earth's surface.
During past few years methods were developed to reconstruct negative potentials in the Sturm-Liouville equation through characteristics of a discrete spectrum. Several numerical tests clarify limitations of these methods. The tests show: (1) only the negative part of a potential having negative and positive parts can be reconstructed through characteristics of the negative spectrum of the Sturm-Liouville equation (the potential is multiplied by a suitable factor ω); (2) spectral data for eigenvalues not larger than –Bω 2, B>0, can be used to reconstruct the potential where it is less than –Bω 2; (3) discontinuities of the potential result in deterioration of approximations with the growth of ω.
This chapter contains sections titled: Introduction Method of Harmonic Decomposition A Finite Number of Harmonics in Noise Two Harmonics at Closely Spaced Frequencies Conclusions Appendix
Creepex, which is the difference between Ms and the orthogonal regression of Ms on mb, is used as a spectral characteristic of seismic sources. Creepex precision is estimated from U.S. Geological Survey Earthquake Data Report data. The difference between the source spectra for subduction and spreading zones is shown to be statistically significant by using A. M. Dziewonski's centroid-moment tensor catalog. The spectra are also different for two continuous zones with different spreading rates. Creepex behavior is studied in relation to a source mechanism parameter (plunge of the null axis) for spreading and subduction zones.
It is becoming increasingly apparent that the crust of the Earth is a critical system, which specifically precludes the deterministic prediction of the magnitude, time, and place of future large earthquakes. A new understanding of the prefracturing deformation of crustal rock suggests an alternative approach. The progress towards fracture-criticality, when the cracking is so extensive that the percolation threshold is reached and earthquakes can occur, can be monitored by analyzing seismic shear-wave splitting. Assuming a reasonably constant input of stress, the time when the effects of increasing stress on the crack distributions in the crust reach levels of fracture-criticality can be estimated and the time and the magnitude, but not necessarily the location of a future large earthquake can be stress-forecast. The effects have been seen with hindsight on many occasions before both earthquakes and volcanic eruptions. Recently, the time and magnitude of an mb = 5 earthquake in SW Iceland has been successfully stress-forecast, within a comparatively narrow error-defined time and magnitude window. Using small earthquakes as the source of shear waves to monitor the rock mass as in SW Iceland requires a nearly continuous swarm of small earthquakes within the shear-wave window of seismic stations together with rapid location and analysis procedures. Such facilities are found probably uniquely in SW Iceland. Swarms of small earthquakes elsewhere are extremely uncommon and are not found when needed near earthquake-vulnerable cities. Stress-forecasting earthquakes on demand requires controlled source seismology, and the first Stress-Monitoring Site (SMS) is currently being set up in 1 km-deep boreholes in the Tjörnes Fracture Zone at Húsavík in northern Iceland. Such SMSs could be set up at any site of the hazard of earthquakes or volcanic eruptions.
A nonlinear integral rheological model is proposed to describe the rheology of the earth's mantle. For constant stress the model behaves like a power law non-Newtonian fluid. However, the model differs significantly if stress changes with time, because it has a memory, in contrast with the power law fluid model. The proposed model is applied to linear stability analysis of large-scale convective circulation in the mantle. The Lorenz equations, a three-mode spatial Fourier expansion of the non-linear thermal convection equations, are generalized for non-Newtonian fluid models. In the proposed rheological model, the instability of the lower thermal boundary layer of a whole mantle convective circulation is oscillatory. The period of the boundary layer convective oscillation is about 6×107 years.
The paper discusses some issues arising out of attempts to calculate and score regular regional forecasts for earthquake probabilities. Given a conditional intensity model for earthquake occurrence, the model is first used to simulate occurrence patterns over the forecast interval. Then the simulations are used to estimate the required occurrence probabilities. A simple binomial score is suggested for monitoring and evaluating the performance of the probability forecasts. It is shown that an upper bound for the average score is provided by the information (or entropy) rate of the model. Similarly the improvement in the score over a standard model (constant rate Poisson with independent magnitudes) is limited from above by the entropy gain. Rates can be per unit time or per event. The performances of the ETAS and Stress Release models are described, and used to illustrate how the efficiency of the forecasts depends on the type of model, the timing of the forecasts and the choice of forecast interval.
The observed intermediate-term variations in earthquake sequences count in favor of precursory activation. This phenomenon forms the basis of an earthquake prediction algorithm known as M8. That this approach is efficient has been demonstrated by many years of its application. However, the M8 algorithm is not optimal, nor is the choice of parameters for it the only one possible. This study proposes a modification of one of the algorithm functionals, which is inversely proportional to the criterion for main rupture (Zhurkov's criterion). Calculations were performed for the existing version under certain assumptions. We list and examine results obtained by testing the modified algorithm on the great earthquakes occurring along the Pacific seismic belt.
We consider a spherical shell of a viscous fluid modeling the outer core of the Earth. We construct a basis consisting of Laplacian eigenfields vanishing at the boundaries of the shell. It is shown that the Laplacian eigenfields ordered by their (increasing) eigenvalues, are also ordered in the same way by their oscillatory vigor. This basis is also used for a simple proof (based on the Carleman theorem) demonstrating that the eigenfields and associated fields of the operator in the problem of free oscillations of a viscous spherical shell under small deviations from solid-body rotation constitute a complete set.
The model of block structure dynamics is studied to find the phenomenon of long-range interaction between synthetic earthquakes. Perfectly rigid blocks separated by thin flat faults are considered in the model. The interaction of blocks along fault planes and with the underlying medium is viscoelastic. The velocity vectors prescribing the motion of structure boundaries and the medium underlying the blocks are model input parameters. When the ratio of stress to pressure exceeds a certain strength level at some part of a fault plane a stress drop (“a failure”) occurs in accordance with the laws of dry friction; it can cause failures in other parts of the same fault or within other faults. In the model, failures represent earthquakes, so a synthetic earthquake catalog is produced. Numerical experiments with a simple block structure favor the existence of long-range interaction between synthetic earthquakes. This conclusion follows from the statistical analysis of synthetic earthquake catalogs. Moreover, an increase of the strength level at a fault ruling out earthquakes that could otherwise occur there significantly affects earthquake flows on other faults. This means that the long-range interaction found in the observed seismicity could be explained by considering lithosphere blocks being perfectly rigid in comparison with fault zones and the underlying medium.
This chapter contains sections titled: Introduction Reduction to the Matrix Sturm-Liouville Problems The Structure of Permissible Matrix Potentials Determination of the Matrix D Related to the Potential A From (10) Relation Between Boundary Conditions and the Matrix D Symmetry in the Relation of Solutions for the Adjoint Systems
